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Q: Katalin rides her bike through a tunnel shaped like the top half of an ellipse. The tunnel is 11 met...

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Q: 19. Differentiate the following functions. a) y = (3t2 + 2)(3t² – 2t + 1) 12-4t+4 t2-5t+6 b) s=

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Q: Given cost and price (demand) functions C(q) = 100q + 43,000 and p(q) = - 2q + 880, what profit can ...

A: Given :cost price (demand) functions C(q)=100q+43000 andp(q)=-2q+880, company earn by selling 50 ite...

Q: 8. Sketch the graph of the following piecewise-defined functions. (-2, if x 0 St² +4, if t -4 a) f(...

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Q: A triangle having an area of 22.62 cm2 is inscribed in a circle whose radius is 6 cm. If one of the ...

A: Given query is to find perimeter of the triangle.

Q: What is a singular solution? Give an example.

A: Singular solution of the differential equation is the solution which can not be obtained from the ge...

Q: Acceleration of a Car The distance s (in feet) covered by a car t seconds after starting is given by...

A: Given problem:- Acceleration of a Car The distance s (in feet) covered by a car t seconds after star...

Q: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and lengt...

A: A rectangular parallelepiped with an altitude of 10cm has its width decreasing by 2 cm/min and lengt...

Q: Assume that you can contribute $7,000 per year into a retirement fund that grows at a constant rate ...

A: Let ,Time = t P = $7,000 Rate = 7% = 0.07 P'(t) = dP/dt (a) Write a first-order linear differential ...

Q: Eliminate ARBITRATY CONSTANTS y = a²t² ; x =b + at

A: Given:To Eliminate ARBITRATY CONSTANTS y = a²t² ; x =b + atSince  we know that, number of independen...

Q: Integration by parts. cos?x –dx sin4x

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Q: cos² x d.x 4 sin* x 2.

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Q: The figure is the graph of the derivative, f', of a function f on [-4, 2]. Determine the intervals o...

A: Topic:- calculus and application of derivatives

Q: 25 The function f is shown below. What is the value of i/ f(x) dx? Write your -4 answer in simplest ...

A: This question is related to definite integration, we will solve it using given information. 

Q: Use the difference an+1 - an to show that the sequence {n – 9"t0 Sn=1 is strictly increasing or stri...

A: Topic   Function decreasing and increasing  Given function is strictly decreasing.     

Q: Find the area of the shaded region. y 20 (1, 7e) 15 y = 7e* 10 5 y=7xe* X -1.0 -0.5 0.5 1.0 1.5 2.0

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Q: Find the Taylor polynomials of orders n = 0,1,2,3 , and 4 about x = xo, and then find the nth Taylor...

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Q: 4,5in3x =sinx S Sinx(sin?x-\= sin?x. Sinx(sinx-1). COS X tank (sin zx - COS tan-o TT

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Q: The motion (s) of a particle can be expressed as a function of time (t). The first derivative of s w...

A: Given

Q: Using the fomat of dy/dx below, find (A +B+C+ D). dy 40t? + At +B dx -Ct? + Dt + 3 ||

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Q: Volume of a Cube The volume V of a cube with sides of length x in. is changing with respect to time....

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Q: INTEGRAL CALCULUS ACTIVITY 3 GENERAL INSTRUCTIONS: 1. Find the Indefinite Integral 2. Show your solu...

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Q: Recall how to identify the limit and exact value of each function givenc using a graph. Given the gr...

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Q: If a cup of coffee has temperature 100°C in a room where the ambient air temperature is 20°C, then, ...

A: Solve for average temperature after 40 min. 

Q: Use the trapezoidal rule with n = 5 to approximate %3D 5 cos(x) -d.x 1 Keep at least 2 decimal place...

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Q: 21. Find y' using implicit differentiation. a) In (xy + x + y) = 2 b) In (sin xy) = xy

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Q: sec x dx 2. Vcot x

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Q: The integral -8 sin(x) cos(x) dx can be evaluated in four different ways: (1) The substitution u = c...

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Q: The population of a city is 45,000. The city grows continuously by 2.8% per year. If this trend cont...

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Q: If a cup of coffee has temperature 100°C in a room where the ambient air temperature is 20°C, then, ...

A: Given query is to find the average temperature of the coffee in the first 40 min.

Q: • Solve the separated functions when (i) k = 0 (ii) k #0 a²x kX(x) = 0 a2x2 %3D

A: For (i), k=0.     ∂2X∂x2-kX=0⇒∂2X∂x2=0Integrating once,⇒∂X∂x=c1Integrating again,⇒X=c1x+c2

Q: For the polynomial below, 2 is a zero. f(x) = x + 2x - 7x - 2 Express f (x) as a product of linear f...

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Q: sin x 5 2 0, cos x

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Q: Given the function f'(x) = x(xxt 4)(x – 5)³, what conclusion can be drawn directly from the sign cha...

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Q: Let us try to find where a function is increasing or decreasing given the following.  f(x) = x3−4x,...

A: Topic:- calculus

Q: Integrate (2x - 5) with respect to x from x = 2 to x = 5.

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Q: Consider you are given the following 10 decimals: .3 .75 .8 .650 .15 .2 .35 .45 .400 .350 Use each d...

A: This question is based on hit and trial.

Q: B. A discrete random variable X has the lollowing probability distribution: 1 1 2 P(X) y 9. 9. 1. Fi...

A: use the basic  property of probability 

Q: Chau can choose Plan A or Plan B for his long distance charges. For each plan, cost (in dollars) dep...

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Q: Integration by parts. cos?x sin4x

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Q: 25. Evaluate the following definite integrals. e) L, 3wv4 – w2 dw

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Q: 2. Let R = {(1, b) ERX R: there is an integer k such that a – b = 2kn}. Prove that R is an equivalen...

A: us the definition of reflexive , symmetric and transitive property of relation to prove it is equiva...

Q: following

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Q: Given the graph of the cosine function f (x) = cos x, evaluate the following limits: 27 ........ -1 ...

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Q: dx 9x2 - 12x-5

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Q: A Norman window consists of a rectangle surmounted by a semicircle. If the perimeter of a Norman win...

A: we should find the height of the rectangle such that the window will admit the most light.

Q: 19. Differentiate the following functions. c) y = Vx ++ Vã sec (x³+1) cos ya d) y =

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Q: 20. Which of the following statements are FALSE? dy 2л -5 I If y = In (7 - 5x), then de 7 - 5x 3e3x ...

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Q: 4. State the domain and range of the following functions. a) у%3D 5х —4 b) y= Vx-x c) ((x,y)ly = vx²...

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Q: Refer to the figure and find the volume V generated by rotating the given region about the specified...

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